In order to make this argument, you will need to think of the French and Indian War as part of the larger, worldwide Seven Years' War.  You will also need to think of financial, as opposed to physical, sacrifice. When looked at in these ways, the war demanded more sacrifices on the part of the people in England.

The Seven Years' War is said to have costed Britain 161 million pounds. Although comparison to today's money is difficult to do with accuracy, this can be estimated to be in the region of $29 billion.  This was a huge sum of money.  This money was raised by taxing the people in Britain, not those in America.

Of course, the colonists in America would not have seen things this way.  They would have focused on the costs of the North American part of the war exclusively.  They would have also focused on the fact that many of them were fighting and dying in the war.  But from the British perspective, the financial costs of the whole war (and the fact that many Britons died worldwide) would have seemed more important.

For these reasons, the British would have felt that they bore more of the burden in this war.  This would have contributed to their feeling that the colonists should be made to pay for some of the costs of the war.

Did the Colonists sacrifice more than the British in the French and Indian War?

While both sides bore enormous sacrifices during the French and Indian War, the Colonists in North America were at greater risk. The British spent more money, but a higher percentage of Colonists fought in the war.

One of the major factors was the smaller population of the Colonies compared to Britain. With fewer soldiers available, every life lost was a greater cost to the Colonies, while the British could easily send for more men. The Colonists lost many of their working men, decreasing their ability to farm and build; the remainder had to take up the slack with little training or impetus.

Another factor was the wealth of the two groups; the British spent more but had a higher base of wealth and influence on which to draw, while the Colonists were still establishing their nation and had fewer accessible resources and money. The Colonists had their economy disrupted, causing setbacks in the national process.

Both sides were hit hard during the war, but the established nation of Britain was in a better position to absorb and weather the loss of men and money than the fledgling Colonies.